My spirits have been bound to me, so do I need to carry around their vessels all the time? I have kept the first spirits I got with me almost day and night (not complaining at all!) but I was wondering if that was something I have to keep doing past the initial 30 days?

Also, should I make a nice place to keep them in, like a fancy box or cabinet? I just want to make sure I do right by them. You know, be able to give back even a part of the love they've given me.

Another question I have about the vessels, is it disrespectful to make the vessels into jewelry?

I keep my Spirits vessels in a nice/pretty wood box they had chose for safe keeping-but they did give me permission to put them on a chain or cord to wear if needed!

A few of my vessels are gemstone bracelets, few are artisan glass I have my own cords for, and I sometimes put my tumbled gemstones into a necklace made for that! So I guess it all depends on your intent and what your spirits wish :) Just double check with them if you’re unsure if its disrespectful or not! But otherwise, I personally dont think its disrespectful, and to me seems to be a bit of a neato way to bond.

My spirits have been bound to me, so do I need to carry around their vessels all the time?

Did you mean it got bridged to you? If so, you don't always have to.

I believe the first initial 30 days is the period of energy adjustment and how you can feel the companion(s)'s presence in that time or after, I don't think you need to get that strict with the vessel though. Rather, go meditating with the vessel, and do invocation. I usually do that in the night before bed. Don't forget to talk with your companion(s) whether telepathically or outspoken.

Also, should I make a nice place to keep them in, like a fancy box or cabinet?

If you can afford them, do that. As long as you're not burdened. Pretty sure your companion(s) will accept any of your offer as long as it's sincere and decent. Btw, you maybe could prepare an altar. So you can put offerings there and your companion(s) got place that won't be disturbed by random stuff.

If they're bridged, you don't need the vessel with you. If they're bound, then you wouldn't have a vessel at all, since it's bound to you and not an inanimate object.